Remark 1.10 For a generic \(Y \in {\rm Gr}_{k,k+m}\) , the ray issued from almost all vectors of \(V_{Y}\)  intersects the simplices of \(P\left(Y,\mathcal {Z}\right)\)  only in their \(m\) -dimensional interior. Pick \(Y\)  generic enough and such a vector, say \(Z_{*}\) , in \(V_{Y}\) . Then the degree of \(f\)  is given by the number of simplices intersecting the ray issued from \(Z_{*}\)  weighted by a sign corresponding to the orientation of the simplex. We recover in these cases the definition of the winding number of [1]}.

